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Number Theory: Arithmetic in Shangri-La
This volume is based on the successful 6th China–Japan Seminar on number theory that was held in Shanghai Jiao Tong University in August 2011. It is a compilation of survey papers as well as original works by distinguished researchers in their respective fields. The topics range from traditional analytic number theory — additive problems, divisor problems, Diophantine equations — to elliptic curves and automorphic L-functions. It contains new developments in number theory and the topics complement the existing two volumes from the previous seminars which can be found in the same book series. Contents:On Jacobi Forms with Levels (Hiroki Aoki)Additive Representation in Thin Sequences, VI...
Zeta Functions, Topology and Quantum Physics
This volume contains papers by invited speakers of the symposium "Zeta Functions, Topology and Quantum Physics" held at Kinki U- versity in Osaka, Japan, during the period of March 3-6, 2003. The aims of this symposium were to establish mutual understanding and to exchange ideas among researchers working in various fields which have relation to zeta functions and zeta values. We are very happy to add this volume to the series Developments in Mathematics from Springer. In this respect, Professor Krishnaswami Alladi helped us a lot by showing his keen and enthusiastic interest in publishing this volume and by contributing his paper with Alexander Berkovich. We gratefully acknowledge financial support from Kinki University. We would like to thank Professor Megumu Munakata, Vice-Rector of Kinki University, and Professor Nobuki Kawashima, Director of School of Interdisciplinary Studies of Science and Engineering, Kinki Univ- sity, for their interest and support. We also thank John Martindale of Springer for his excellent editorial work.
Number Theory: Plowing and Starring Through High Wave Forms
Based on the successful 7th China–Japan seminar on number theory conducted in Kyushu University, this volume is a compilation of survey and semi-survey type of papers by the participants of the seminar. The topics covered range from traditional analytic number theory to elliptic curves and universality. This volume contains new developments in the field of number theory from recent years and it provides suitable problems for possible new research at a level which is not unattainable. Timely surveys will be beneficial to a new generation of researchers as a source of information and these provide a glimpse at the state-of-the-art affairs in the fields of their research interests. Contents:O...
Contributions to the Theory of Zeta-Functions
This volume provides a systematic survey of almost all the equivalent assertions to the functional equations - zeta symmetry - which zeta-functions satisfy, thus streamlining previously published results on zeta-functions. The equivalent relations are given in the form of modular relations in Fox H-function series, which at present include all that have been considered as candidates for ingredients of a series. The results are presented in a clear and simple manner for readers to readily apply without much knowledge of zeta-functions. This volume aims to keep a record of the 150-year-old heritage starting from Riemann on zeta-functions, which are ubiquitous in all mathematical sciences, wherever there is a notion of the norm. It provides almost all possible equivalent relations to the zeta-functions without requiring a reader's deep knowledge on their definitions. This can be an ideal reference book for those studying zeta-functions.
Vistas of Special Functions II
This book (Vista II), is a sequel to Vistas of Special Functions (World Scientific, 2007), in which the authors made a unification of several formulas scattered around the relevant literature under the guiding principle of viewing them as manifestations of the functional equations of associated zeta-functions. In Vista II, which maintains the spirit of the theory of special functions through zeta-functions, the authors base their theory on a theorem which gives some arithmetical Fourier series as intermediate modular relations OCo avatars of the functional equations. Vista II gives an organic and elucidating presentation of the situations where special functions can be effectively used. Vist...
Contributions To The Theory Of Zeta-functions: The Modular Relation Supremacy
This volume provides a systematic survey of almost all the equivalent assertions to the functional equations — zeta symmetry — which zeta-functions satisfy, thus streamlining previously published results on zeta-functions. The equivalent relations are given in the form of modular relations in Fox H-function series, which at present include all that have been considered as candidates for ingredients of a series. The results are presented in a clear and simple manner for readers to readily apply without much knowledge of zeta-functions.This volume aims to keep a record of the 150-year-old heritage starting from Riemann on zeta-functions, which are ubiquitous in all mathematical sciences, wherever there is a notion of the norm. It provides almost all possible equivalent relations to the zeta-functions without requiring a reader's deep knowledge on their definitions. This can be an ideal reference book for those studying zeta-functions.
Number Theory
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Number Theory
This volume aims at collecting survey papers which give broad and enlightening perspectives of various aspects of number theory. Kitaoka's paper is a continuation of his earlier paper published in the last proceedings and pushes the research forward. Browning's paper introduces a new direction of research on analytic number theory ? quantitative theory of some surfaces and Bruedern et al's paper details state-of-the-art affairs of additive number theory. There are two papers on modular forms ? Kohnen's paper describes generalized modular forms (GMF) which has some applications in conformal field theory, while Liu's paper is very useful for readers who want to have a quick introduction to Maa...
Multiple Zeta Functions, Multiple Polylogarithms and Their Special Values
This is the first introductory book on multiple zeta functions and multiple polylogarithms which are the generalizations of the Riemann zeta function and the classical polylogarithms, respectively, to the multiple variable setting. It contains all the basic concepts and the important properties of these functions and their special values. This book is aimed at graduate students, mathematicians and physicists who are interested in this current active area of research. The book will provide a detailed and comprehensive introduction to these objects, their fascinating properties and interesting relations to other mathematical subjects, and various generalizations such as their q-analogs and the...
